Duffy has not recovered from the cracked cheekbone he picked up against Munster in the Magners League on December 26. He will be out for at least two more weeks.
However, Ireland 'A' prop Brett Wilkinson will be in contention to start against Montpellier, having recovered from a hand injury.
Connacht have played a record 88 Challenge Cup matches - and are the only team to have been present in all 14 seasons of the competition - but it is game number 89 that really counts.
Their coach Michael Bradley is hoping the home fans turn out in huge numbers as the westerners look to tighten their grip on Pool 2 and reach the quarter-final stage.
"Hopefully, we will get a great crowd and that we can get the win which will take us into the quarter-finals," he said.
"It is going to be one of those days on which our season will be judged. We are very conscious of that fact.